Cox was not run immediately. Looks like he was given plenty of leeway. Cooper walked away once and was getting ready to walk again when he dumped Cox. Right after the ejection, about 1:20 in the vid, you can see Cooper tell Cox something like " I told you what I did. I'm just being honest with you." From what I can gather, Cooper ate crow, admitted his mistake and Cox continued thus the ejection.
Baseball Video Highlights & Clips | ATL@LAD: Cox is ejected for arguing with the ump - Video | MLB.com: Multimedia